1. Field of the Invention
The present invention relates to frequency compensated amplifiers, and in particular, to amplifier circuits with Miller-effect frequency compensation.
2. Description of the Related Art
Miller feedback is commonly used to compensate multistage amplifiers. By adding a feedback capacitance around an intermediate amplifier stage phase compensation is provided by introducing a pole-zero cancellation. As is well known, due to the Miller effect, a response zero is developed in the amplifier stage having the feedback capacitance such that the response zero is coincident with the pole of the succeeding amplifier stage.
A drawback of Miller feedback is a poor power supply rejection ratio (PSRR). At high frequency, standard Miller feedback causes the PSRR to begin to degrade at the dominant pole frequency. This can be improved, as shown by Ribner and Copeland in xe2x80x9cDesign Techniques for Cascoded CMOS Op Amps With Improved PSRR and Common Mode Input Rangexe2x80x9d, IEEE JSSCC December 1984 (Ribner et al., incorporated herein by reference), by feeding the Miller capacitance back to a low impedance node. This method provides a significant improvement to the PSRR. However, it also creates two complex poles at high frequency that often cause the amplifier to be unstable.
Referring to FIG. 1, a folded cascode amplifier has been proposed using a modified Miller feedback as described by Ribner et al. Capacitor C2 is traditionally used to compensate the Miller loop. For the following discussion, it is assumed that capacitor C2 is significantly larger than the gate-to-source capacitance CGS of transistor M4. In cases where this is not true, a low input capacitance buffer (not shown), such as a source follower, can be connected between node N1 and the gate terminal of transistor M4 to reduce the capacitive loading on the high impedance node N1 by transistor M4. (In the Figures and throughout the following discussion, transistors M1, M2, M3, M4, M5, M6, M7, M8 are insulated gate field effect transistors, such as P-type and N-type metal oxide semiconductor field effect transistors (P-MOSFETs and N-MOSFETs), and are depicted using conventional transistor symbols for P-MOSFETs and N-MOSFETs.)
Referring to FIGS. 2 and 3, there are two loops in the system that need to be analyzed. The first is the traditional DC loop as depicted in FIG. 2. The loop characteristics of this DC system are well known in the art and, therefore, need not be analyzed here. The second is the Miller feedback loop as depicted in FIG. 3. As is well known, when analyzing the Miller loop, the inputs to the DC loop are AC grounded. In this way, the characteristics of the Miller loop can be determined independently of the DC loop. Capacitor C1 creates a zero at DC and a dominant pole due to the high impedance of node V3 reflected through transistor M1. The Miller loop also has two low frequency poles at nodes V3 and Vout due to capacitors C2 and C1. It is these two poles that converge when the Miller loop is closed, thus giving rise to a pair of complex poles in the DC loop. Eliminating one of these poles would significantly improve the loops"" stability.
Referring to FIG. 4, the Miller loop can be simplified as shown. Referring to FIG. 5, this circuit can be modeled to a first order as shown. For simplicity, the capacitance of capacitor C1 is set to A times the capacitance of capacitor C2 (Equation 0). The loop transmission can be characterized by Equation 1. As expected, the cascode portion of the loop contributes a DC zero, and two poles, while the output stage contributes a single pole as expressed by Equation 2.
c1"khgr"AC2"khgr"ACxe2x80x83xe2x80x83Equation 0:
      Equation    ⁢          xe2x80x83        ⁢    1    ⁢          :        ⁢                  V        o                    V        i              =            [                        (                      sAC            ⁢                          xe2x80x83                        ⁢                          (                                                gds                  1                                +                                  gm                  1                                +                                  gmb                  1                                            )                                )                          (                                                    (                                                      gds                    2                                    +                                      gds                    1                                    +                  sC                                )                            ⁢                              xe2x80x83                            ⁢                              (                                                      gds                    3                                    +                                      gds                    1                                    +                                      gm                    1                                    +                                      gmb                    1                                    +                  sAC                                )                                      -                                          (                                  gds                  1                                )                            ⁢                              xe2x80x83                            ⁢                              (                                                      gds                    1                                    +                                      gm                    1                                    +                                      gmb                    1                                                  )                                              )                    ]        ⁢          "AutoLeftMatch"              [                              -                          gm              4                                                          gds              4                        +                          s              ⁢                              xe2x80x83                            ⁢                              (                AC                )                                                    ]                  Equation    ⁢          xe2x80x83        ⁢    2    ⁢          :        ⁢          xe2x80x83        ⁢          ω      p3        ≈            gds      4        AC  
Finding the poles of the cascoded stage is somewhat more involved. Using the standard form for solving the roots of a second order equation produces Equations 3-9. Equation 10 is presented as a compact expression for the total Miller loop system response.       Equation    ⁢          xe2x80x83        ⁢    3    ⁢          :        ⁢          xe2x80x83        ⁢    r    =                    -        b            ±                                    b            2                    -                      4            ⁢            ac                                      2      ⁢      a      xe2x80x83b2"khgr"gds1AC+2gds1(gds3+gds1+gm1+gmb1)AC2+((gds3+gds1+gm1+gmb1)2C2xe2x80x83xe2x80x83Equation 4:
4ac"khgr"4AC2(gds2gds3+gds2gds1+gds2(gm1+gmb1)+gds3gds1)xe2x80x83xe2x80x83Equation 5:
b=(gds1AC+(gds3+gds1+gm1+gmb1)C)xe2x80x83xe2x80x83Equation 6:
2a=2AC2xe2x80x83xe2x80x83Equation 7:
      Equation    ⁢          xe2x80x83        ⁢    8    ⁢          :        ⁢          xe2x80x83        ⁢          ω      p1        =                    (                                            gds              1                        ⁢                          xe2x80x83                        ⁢            AC                    +                                    (                                                gds                  3                                +                                  gds                  1                                +                                  gm                  1                                +                                  gmb                  1                                            )                        ⁢                          xe2x80x83                        ⁢            C                          )                    2        ⁢                  AC          2                      -                                                      gds              1                        ⁢                          xe2x80x83                        ⁢            AC                    +                      2            ⁢                          gds              1                        ⁢                          xe2x80x83                        ⁢                          (                                                gds                  3                                +                                  gds                  1                                +                                  gm                  1                                +                                  gmb                  1                                            )                        ⁢                          xe2x80x83                        ⁢                          AC              2                                +                                                    (                                                      gds                    3                                    +                                      gds                    1                                    +                                      gm                    1                                    +                                      gmb                    1                                                  )                            2                        ⁢                          xe2x80x83                        ⁢                          C              2                                -                      4            ⁢                          AC              2                        ⁢                          xe2x80x83                        ⁢                          (                                                                    gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    3                                                  +                                                      gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    1                                                  +                                                      gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  gm                        1                                            +                                              gmb                        1                                                              )                                                  +                                                      gds                    3                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    1                                                              )                                                  (                  2          ⁢                      AC            2                          )                  Equation    ⁢          xe2x80x83        ⁢    9    ⁢          :        ⁢          xe2x80x83        ⁢          ω      p1        =                    (                                            gds              1                        ⁢                          xe2x80x83                        ⁢            AC                    +                                    (                                                gds                  3                                +                                  gds                  1                                +                                  gm                  1                                +                                  gmb                  1                                            )                        ⁢                          xe2x80x83                        ⁢            C                          )                    2        ⁢                  AC          2                      +                                                      gds              1                        ⁢                          xe2x80x83                        ⁢            AC                    +                      2            ⁢                          gds              1                        ⁢                          xe2x80x83                        ⁢                          (                                                gds                  3                                +                                  gds                  1                                +                                  gm                  1                                +                                  gmb                  1                                            )                        ⁢                          xe2x80x83                        ⁢                          AC              2                                +                                                    (                                                      gds                    3                                    +                                      gds                    1                                    +                                      gm                    1                                    +                                      gmb                    1                                                  )                            2                        ⁢                          xe2x80x83                        ⁢                          C              2                                -                      4            ⁢                          AC              2                        ⁢                          xe2x80x83                        ⁢                          (                                                                    gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    3                                                  +                                                      gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    1                                                  +                                                      gds                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  gm                        1                                            +                                              gmb                        1                                                              )                                                  +                                                      gds                    3                                    ⁢                                      xe2x80x83                                    ⁢                                      gds                    1                                                              )                                                  (                  2          ⁢                      AC            2                          )                  Equation    ⁢          xe2x80x83        ⁢    10    ⁢          :        ⁢          xe2x80x83        ⁢                  V        o                    V        i              =            [                        (                                    gds              1                        +                          gm              1                        +                          gmb              1                                )                ⁢                  xe2x80x83                ⁢                              (                          -                              gm                4                                      )                                gds            4                              ]        ⁢          "AutoLeftMatch"                        [                      sAC                                          (                                  1                  +                                      s                                          ω                      p1                                                                      )                            ⁢                              xe2x80x83                            ⁢                              (                                  1                  +                                      s                                          ω                      p2                                                                      )                                              ]                ⁡                  [                      1                          1              +                              s                                  ω                  p3                                                              ]                    
The pole at frequency xcfx89p1 can be shown to be much lower than the pole at frequency xcfx89p2 and thus of little interest for purposes of this analysis since it is effectively canceled by the zero at DC. Using the assumption expressed by Equation 11 and for moderately low values of the factor A, the expression for the pole at frequency xcfx89p2 can be simplified as shown in Equation 12.
gm≈10gmbs≈100gdsxe2x80x83xe2x80x83Equation 11:
      Equation    ⁢          xe2x80x83        ⁢    12    ⁢          :        ⁢          xe2x80x83        ⁢          ω      p2        ≈      b    a    ≈            (                                    gds            1                    ⁢                      xe2x80x83                    ⁢          AC                +                              (                                          gds                3                            +                              gds                1                            +                              gm                1                            +                              gmb                1                                      )                    ⁢                      xe2x80x83                    ⁢          C                    )              AC      2        ≈            (                                    gds            1                    ⁢                      xe2x80x83                    ⁢          AC                +                              (                                          gm                1                            +                              gmb                1                                      )                    ⁢                      xe2x80x83                    ⁢          C                    )              AC      2        ≈                    gm        1            +              gmb        1              AC    ≈            gm      1        AC  
Referring to FIGS. 6-9, the open loop frequency responses for two nodes in the circuit of FIG. 5 are produced. FIG. 6 depicts the magnitude response as seen from node voltage Vi to node voltage V3, while FIG. 7 depicts the phase response. From this it can be seen that the pole at frequency xcfx89p2 has already degraded the phase margin by 90 degrees. If the pole at the output is sufficiently low, the system will be unstable and exhibit peaking at the unity gain frequency. FIG. 8 depicts the open loop magnitude response from node voltage Vi to node voltage Vo. From this it can be seen that the output pole causes the high frequency rolloff to degrade with two poles before the unity gain frequency. FIG. 8 also depicts the closed loop magnitude response. FIG. 9 depicts the open and closed loop phase response from which it is evident that the phase margin is nearly zero. Therefore, the Miller loop is unstable and will cause severe peaking when inserted in the DC loop.
While the DC loop is not analyzed here in detail, a brief explanation of the effect of the Miller loop can be provided. Referring back to FIG. 1, it is clear that transistor M1 provides a current into the impedance seen at node V2. FIG. 10 depicts the impedance at node V2 when the Miller loop is closed and the DC loop is open. The resonant peak is due to the poorly compensated Miller loop. FIG. 11 depicts the open and closed loop magnitude response of the DC loop. The peaking here is at the same frequency as the peaking in the impedance at node V2, as well as the peaking in the frequency response of the Miller feedback loop. FIG. 12 depicts the open and closed loop phase response of the DC loop. Though not depicted in detail here, it should nonetheless be seen that the phase response of the closed loop system is nearly identical to the phase response of the closed loop Miller feedback system as depicted in FIG. 9.
An amplifier with Miller-effect frequency compensation in accordance with the presently claimed invention includes a high frequency zero that cancels one of the high frequency complex poles thereby leaving one real pole. Cancellation of such pole significantly improves the bandwidth and stability of the Miller feedback system, and can be accomplished with consistency over PVT (variations in fabrication processes P, power supply voltage V and temperature T). In accordance with the presently claimed invention, the Miller feedback capacitor is connected to an internal terminal of the amplifier having a low impedance, and shunt compensation circuitry is connected to an intermediate signal terminal that drives the output amplifier stage. The compensation circuitry, which includes serially coupled capacitive and resistive circuit elements, introduces a high frequency zero to cancel one of the high frequency complex poles introduced by the Miller feedback capacitor connection.
In accordance with one embodiment of the presently claimed invention, an amplifier with Miller-effect frequency compensation includes first and second amplification circuitry, feedback capacitance and compensation circuitry. The first amplification circuitry, including an internal terminal and a first output terminal, receives and amplifies an input signal to provide a first amplified signal via the first output terminal. The internal terminal has an internal terminal impedance associated therewith, the first output terminal has an output terminal impedance associated therewith, and the internal terminal impedance is substantially lower than the output terminal impedance. The second amplification circuitry, coupled to the first output terminal and including a second output terminal, receives and further amplifies the first amplified signal to provide a second amplified signal via the second output terminal. The feedback capacitance is coupled between the second output terminal and the internal terminal. The compensation circuitry is coupled in shunt to the first output terminal and includes capacitive and resistive circuit elements mutually coupled in series.
In accordance with another embodiment of the presently claimed invention, an amplifier with Miller-effect frequency compensation includes first and second power supply terminals, first and second amplification circuitry, feedback capacitance and compensation circuitry. The first amplification circuitry, coupled between the first and second power supply terminals and including an internal terminal and a first output terminal, receives and amplifies an input signal to provide a first amplified signal via the first output terminal. The internal terminal has an internal terminal impedance associated therewith, the first output terminal has an output terminal impedance associated therewith, and the internal terminal impedance is substantially lower than the output terminal impedance. The second amplification circuitry, coupled between the first and second power supply terminals and to the first output terminal and including a second output terminal, receives and further amplifies the first amplified signal to provide a second amplified signal via the second output terminal. The feedback capacitance is coupled between the second output terminal and the internal terminal. The compensation circuitry is coupled between the first output terminal and the first power supply terminal and includes serially coupled capacitive and resistive circuit elements.
In accordance with still another embodiment of the presently claimed invention, an amplifier with Miller-effect frequency compensation includes first and second amplifier means, feedback means and shunting means. The first amplifier means is for receiving a feedback signal, receiving and amplifying an input signal and providing a first amplified signal. The second amplifier means is for receiving and further amplifying the first amplified signal and providing a second amplified signal, wherein the first and second amplifier means together have a transfer function associated therewith. The feedback means is for selectively feeding back the second amplified signal as the feedback signal to the first amplifier means, thereby introducing to the transfer function one or more high frequency complex poles. The shunting means is for selectively shunting the first amplified signal, thereby introducing to the transfer function at least one high frequency zero that substantially cancels one of the one or more high frequency complex poles.
In accordance with yet another embodiment of the presently claimed invention, an amplifier with Miller-effect frequency compensation includes first and second amplifier means, feedback means and shunting means. The first amplifier means is for receiving a feedback signal, receiving and amplifying an input signal and providing a first amplified signal. The second amplifier means is for receiving and further amplifying the first amplified signal and providing a second amplified signal. The feedback means is for selectively feeding back the second amplified signal as the feedback signal to the first amplifier means. The shunting means is for selectively shunting the first amplified signal. Together the first and second amplifier means, the feedback means and the shunting means have associated therewith a transfer function with one or more high frequency complex poles and a high frequency zero which is complementary to one of the one or more high frequency complex poles.